A heap of rubbish in the shape of a cube is being compacted into a smaller cube.

Question

A heap of rubbish in the shape of a cube is being compacted into a smaller cube. Given that the volume decreases at a rate o f4 cubic meters per minute, find the rate of change of an edge, in meters, of othe cube when the volume is exactly 125 cubic meters. -75/4| -4/75| 4| -75| 4/25| A rectangle is inscribed in a circle of radius 6 inches. If the length of the rectangle is decreasing at the rate of 2 inches per second, how fast is the area 11A>> 3 changing at the instant when the length is 6 inches? 11 4 4 75 41degree -751 4 1 25 1

Explanation / Answer

volume of cube v =x3 where x is the length of edge

volume =125 cubic meters

125=x3

=>x=1251/3

=>x =5m

v =x3

differentiate with respect to time t

dv/dt =3x2 dx/dt

fiven volume decreasing at 4cubic meters per min

dv/dt =-4

-4 =3*52dx/dt

-4=75 dx/dt

dx/dt =-4/75

rate of change of length of edge =-4/75 cm/min

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